7 semester

1

Name of disciplines

Equations of mathematical physics

2

Course of Study

4, specialty 1-31 03 01-01 Mathematics (research and production activities)

3

Semester of training

7

4

Amount of credits

2

5

Full name of lecturer

Doctor of Physical and Mathematical Sciences, Professor Lomovtsev Fedor Egorovich

6

Objectives of the study
disciplines

 

Teach students to master the concepts of the theory of elliptic partial differential equations and basic mathematical methods of investigation.

Teach students to solve the boundary value problems of Dirichlet and Neumann for the Poisson equation. As a result of the study, the student should be able to:

– investigate the correctness of the boundary value problems of Dirichlet and Neumann for the Poisson equation;

– use the Green’s function method and the method of separation of variables to solve these boundary value problems.

7

Prerequisites

Mathematical analysis, ordinary differential equations.

8

Content
disciplines

Elliptic equations of mathematical physics. Integral Green’s formulas. Definition and properties of harmonic functions. Statement of the basic boundary-value problems for the Poisson equation. On the uniqueness of solutions of the Dirichlet and Neumann problems. Methods for separation of variables and Green’s functions. Justification of the Fourier method. The method of fictitious charges. Solutions by the Green’s function of the internal and external Dirichlet problems for a ball. Poisson integrals. The Liouville theorem.

9

Recommended
literature

1. Tikhonov A.N., Samarskii A.A. Equations of mathematical physics. Moscow, 2004.

2. Korzyuk V.I. Equations of mathematical physics. Minsk, 2011.

3. Lomovtsev F.E. Equations of mathematical physics. Collection of tasks. Minsk, 2009.

10

Teaching Methods

Problematic, communicative with elements of educational and research activity, controlled independent work.

11

Language of learning

Russian

12

Conditions (requirements),
routine control

– test papers
– colloquiums

13

Form of current certification

Exam